Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180), Hardback Book

Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) Hardback

Part of the Annals of Mathematics Studies series

Description

Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view.

The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject.

The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters.

The basic question considered in the book is how the values of the Mellin transform are distributed (in a probabilistic sense), in cases where the input function is suitably algebro-geometric.

This question is answered by the book's main theorem, using a mixture of geometric, categorical, and group-theoretic methods.

By providing a new framework for studying Mellin transforms over finite fields, this book opens up a new way for researchers to further explore the subject.

Information

  • Format: Hardback
  • Pages: 208 pages
  • Publisher: Princeton University Press
  • Publication Date:
  • Category: Number theory
  • ISBN: 9780691153308

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